Prime Number Distribution Series (PNDS), developed by the NSI team of mathematicians2, computes the exact count of primes below integer N (N → ∞) (π (N)). Aside from divide and count test and various sieving methods, it is believed that PNDS is the first and only exact mathematical formula for finding prime numbers.

PNDS demonstrates that a pattern of prime numbers exists; making fast evaluation of π (N) for large N at record speeds possible2.

Riemann Hypothesis

As shown in the technical paper, neither PNDS nor its inverse is a complex variable function, and that PNDS uniquely produces exact count of prime numbers for a given integer P, where 2 < P < ∞, it may be concluded that the distribution of prime numbers is not a complex variable problem and Riemann Zeta Function may not be pertinent to the subject matter.

History

Little or not at all considered fact is that the distribution of prime numbers can be regarded as piecewise orderly. For example, consider Euler prime formula, P(n) = n2 − n + 41. It is easy to show this function is asymptotic and strictly speaking only holds for 0 < n < 5. Like Euler prime formula, infinitely many series can be formulated each representing prime number distribution at the boundary limits. We therefore conclude that no single series, of any order; equation or a function will ever yield prime numbers for all n = 1 to ∞ exclusively.

Henceforward, Riemann conjecture that the nontrivial zeros of the Riemann zeta function all have real part ½ is an irrelevant submission to the problem.

However, a series can be formulated that will produce the boundary values of the piecewise orderly regions for N → ∞; as given by the PNDS mathematical formula